9/15/2021

Chapter 3

• General multiplication rule (see the bottom of p. 61)
• Independence
  • Consider a sample space S of 5 outcomes {w1, w2, w3, w4, and w5} with probabilities P(w1)=1/8, P(w2)=P(w3)=P(w4)=3/16. Let A={w1, w2, w3} and B={w1, w2, w4} and C={w1, w3, w4}. Show that P(ABC)=P(A) x P(B) x P(C), but that A, B, and C are not pairwise independent.
  • Show that if A, B, C, and D are independent, then AB and CUD are independent.

We will have a problem session on Friday. Please read Sections 4.1, 4.2, 4.3, and 4.4 for class on Monday.